1. Structure of thin films by electron diffraction János L. Lábár

2. Usage of diffraction data in structure determination Identifying known structures Solving unknown structures –Structure determination Unit cell dimensions Space group symmetry Unit cell content (atoms and their appr. coordinates) –Structure refinement More accurate atomic coordinates Validation of the structure (attainable match)

3. Structure determination Periodic functions  Fourier coefficients –Amplitude : diffraction  the phase problem –Phase : real space (HRTEM, fragment) reciprocal space (Direct methods) Single crystal diffraction –X-rays, neutrons  electrons Powder diffraction –X-rays, neutrons  electrons

4. Single crystal diffraction Tilting experiments Identification of reflections: indexing –Unit cell dimensions –Space group symmetry (XRD, SAED, CBED) Integration of individual intensities –Background Phases (real  reciprocal space) –Dynamic intensities in SAED

5. Single crystal diffraction XRD: –Up to 2000 atoms in the asymmetric unit –Up to 100 atoms: guaranteed success –Rule of thumb: # refl > 10 * # atoms SAED: –CRISP, ELD  Direct methods (EDM) –Dynamic intensities in SIR97 –Up to 30 atoms in the asymmetric unit –Size, image

6. Powder diffraction Collapse of 3D into 1D –Types: Equivalent reflections, multiplicity Exact overlap: e.g. ( 43l )  ( 50l ) in tetragonal Accidental: within instrumental resolution –Indexing programs –Peak decomposition La Bail Pawley

7. Powder diffraction Degree of overlap: Resolution Background Instability: negative peaks / oscillating int. XRD (+ refinement from neutrons) : –Synchrotron: 60 atoms in asymmetric unit –Laboratory:  30 atoms in asymmetric unit Neutron: better for refinement SAED: instrumental resolution limit, BKG

8. Powder diffraction: SAED resolution (peak width) Beam convergence Elliptical distortion OL spherical aberration  size of selected area

9. Powder diffraction: SAED elliptical distortion

10. Powder diffraction: SAED spherical aberration

11. Powder diffraction: Pattern decomposition with ProcessDiffraction Background –Normal, log-Normal –Polynomial, Spline Peak shapes –Gaussian, Lorentzian –Pseudo-Voigt Global minimum –Downhill SIMPLEX –Manual control Example: Al + Ge: SAED on film –Large crystal Al: Gaussian –Small crystal Ge: Lorentzian

12. Pattern decomposition with ProcessDiffraction

13. Structure refinement: The Rietveld method Start from assumed structure Least-square fitting of whole-pattern Fitting parameters: –Scale-factor –Atomic positions –Temperature factors –Cell parameters –Peak shape parameters (instrumenal  sample) –Background –Additional peaks (phase)

14. The Rietveld method Most known structures from Rietveld refinement Scaling factors  Quantitative phase analysis (volume fractions) Neutrons: no angle dependence  best for refinement Resolution (peak width) is less important  SAED can also be used efficiently for refinement SAED: Cell parameters  camera length

15. Quantitative phase analysis for nanocrystalline thin films from SAED Example: 100 Å Al + 100 Å NiO Measured volume fraction by ProcessDiffraction: 51% Al + 49% NiO Fitted parameters: peak parameters, L, scaling factors, DW

16. Structure refinement from SAED Integrated intensities: –ELD –ProcessDiffraction Refinement: –FullProf –ProcessDiffraction Simple example: TiO 2 – Anatase –Selection of origin  transform „z” before compare

17. Structure refinement with ProcessDiffraction Structure definition modul –Checks: coordinates  site symmetry Options modul checks –if selected site is „refinable” (variation of coordinate value does not change site symmetry) –If selected options are reasonable Cross-checking for nanocrystalline samples –Pair correlation function (different models  measured)

18. ProcessDiffraction: Options for refinement

19. Structure refinement with ProcessDiffraction Example: Anatase 4 nm powder Acceptable match Refined position of oxygen: z=0.217 Compare to z=0.2064 (Pearson’s) z=0.2094 (Weirich transformed)

20. Is the example result acceptable? Independent test Pair correlation function –Measured –Calculated for both structures Refined result is in agreement with g(r)

21. Remarks to refinement Nanocrystalline films are strained Exact shape and size of the background is ambiguous in electron diffraction Refined position is also a function of refined cell dimensions (accurate calibration of camera length)

22. Conclusions: structure of thin films by electron diffraction Phase identification from both single crystal and powder patterns Quantitative phase analysis from nanocrystalline powder patterns Structure determination from single crystal patterns (SAED, CBED) Structure refinement from nanocrystalline powder patterns Limits are still to be examined